Chvorinov’s rule

The amount of heat which has to be emitted by a casting to the mold during solidification is directly proportional to the weight of the casting and the chosen superheat. In 1940, the idea that heat can only be emitted via the contact surfaces touching the mold led Nicolas Chvorinov to conclude that this influences the solidification time (or solidification rate) in a direct and proportional manner.

Chvorinov’s rule illustrates the relationship between the solidification time of a casting in the mold and its volume or surface dimensions and is as laid down in eq. 1:

Eq. 1:

tE Solidification time in s
k Metal-, mold-material- und temperature-dependent coefficient (s/cm2)
V Casting volume in cm3
A Surface area of the casting in cm2
n Exponent with n = 1.5 to 2.0

Coefficient k can be calculated according to eq. 2:

Eq. 2:

TL Liquidus temperature of the casting material
TA Temperature of the mold material at the beginning of casting
ΔTs Tcasting temperature – TL = melt superheat
L Heat of fusion or heat of solidification
K Thermal conductivity of the mold material
λ Density of the mold material
c Specific thermal capacity of the mold material
ρM Density of the casting material
cM Specific thermal capacity of the casting material

The V/A ratio is also referred to as the solidificationmodulus M (unit cm, see also Modulus, Casting modulus). This designation and a typical exponent of n = 2 gives the solidification time according to eq. 3 with:

Eq. 3:

Therefore, Chvorinov’s rule can be used to verify that the risers solidify at a later time than the casting (or that the casting solidifies prior to the risers) in order to ensure sufficient post-feeding and thus compensation of the solidification shrinkage by the risers.

For this, the solidification time of the risers should, for example, be 25% longer than that of the casting, which results in the following condition according to eq. 4:

Eq. 4

Additional references:
Design of castings
Favorable casting design
Favorable casting engineering
Heuvers’ circle method